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as gbonnet mentioned, submitting to the search engines are not necessary. In all reality if your trying to get your page indexed, it will come a lot quicker if you can get a link on someones page that has a page rank of 3+.

If for any reason you cannot get your site listed in a directory or a friend's site, create a single page that contains links to all of your other pages and sites (site map). Link to your site map from your main page. Submit your site map to Google, and submit your index page to DMOZ under an appropriate category.

Once you're on DMOZ, nearly every crawler and web directory on the planet will find your site within a couple weeks. And once your sitemap is in Google, you'll be getting reindexed quite frequently by the only search engine that really counts anyway ...

The only trouble with DMOZ is that you can wait for months (if not years) before your site is listed ...

I have to agree. I submitted one of my sites twice over a 4 year period and still waiting. Pretty sure I got it in the right category, too. I decided to give up. I thought about being an editor, but just decided to be happy with google.

No it's not necessary, but it sure is recommended.
I always submit to search engines for a speedier and proper indexing (sitemap works best with Google). This way the entire site is indexed and in the system within a week or two at most. DMOZ does take months, true.
Another good way is to post to Google Base. I got my first website indexed in two days this way.

Hey guys. Is there any way to submit the URL of a site to multiple search engines at once? Instead of having to submit with google, yahoo etc. separately.

Thanks,
Kris.

If you want your site to be crawled by search engines the best thing would be to get it linked in a high-ranking website, e.g. high-ranking web directory.
Just submitting your url to google or yahoo will not give you much. It might be indexed, but it won't be seen and searched.